Magic square puzzle



United States Patent 3,189,350 MAGIC SQUARE PUZZLE Bushrod W. Hopkins,RU. Box 123-3, RED. 1, Brookeville, Md. Filed Aug. 15, 1960, Ser. No.49,704 2 Claims. (Cl. 273-453) This invention relates to a recreationaldevice, and in particular to a means for effecting magic squaresolutions, with a minimum of time and eitort, and in a tidy manner.

In particular, the magic squares contemplated are the type known inrecreational mathematics, and in statistical analysis, as Graeco-Latinsquares.

In the Latin square, from which these developed, having n squares on aside, a series of n symbols, such as Latin letters, are so arranged thatno symbol occurs twice in any row or in any column. Many sucharrangements are possible, and from this evolved a more complicatedsquare in which two different arrangements of Latin squares aresuperimposed so that two symbols appear in each small square. It is aconsequence of this arrangement that in addition to the two differentsolutions of the Latin square, a further solution is provided in that notwo-symbol combination appears in any row or in any column. As aconvenience the two Latin squares are made up from two differentfamilies of symbols, such as Greek letters and Latin letters, from whichthe term Graeco-Latin arises, but both may as well be of the same type,such as Latin, Greek, Arabic numerals, or distinct colors.

As reported in the November, 1959 issue of Scientific American magazine,pages 181-188, the problem of the Graeco-Latin square had a vigorousresurgence through the efforts of modern workers who disproved aconjecture of the 18th century mathematician Euler that no solution waspossible for this type of scquare in the cases where the number ofsquares on a side is even and not divisible by 4. This was refuted whena set of solutions were found for a square wherein n=10, and many othershave since been found.

As a consequence, there has developed a renewed interest, not only onthe part of puzzlers, but also in the i 1 design of controlledexperiments, as in agricultural studies. As an indication of how muchmaterial there is to keep a puzzler occupied, it may be stated that, inthe case of a Graeco-Latin square, with n=4, even if the two diagonalsareincluded in the requirement placed on the rows and columns, at least72 different solutions are possible. Since the tools of the averagepuzzler will consist of pen or pencil, and paper, it will be seen thatmuch erasing and superpositioning will be entailed, with consequentconfusion.

It is therefore an object of the present invention to facilitate thetrial-and-error method of solving magic squares. A further object is toaccelerate such solutions, While minimizing untidiness and confusion.More particularly it is an object to provide a system of blocks fortentative stages of solution, wherein a whole column or row may beprepared and placed in a tentative assembly for selection, and also toprovide blocks in composite form for selection of symbol combinations inindividual blocks.

For a detailed description of the invention, reference is made to thefollowing specification, as illustrated in the drawings, in which:

FIGURE 1 is a top plan view of an assembly of 100 blocks in a tray, withthe two-digit combinations arranged in one of the possible solutions,

FIGURE 2 is a bracketed view, showing, in perspective, one of theblocks, and the rod on which such blocks are assembled,

FIGURE 3 is a top plan view of a modified block,

FIGURE 4 is a sectional view taken along the line 4-4 of FIGURE 3.

FIGURE 5 is a view similar to FIGURE 4, showing a modification,

FIGURE 6 is a bottom plan view of the block of FIG- URE 3,

FIGURE 7 is a fragmentary sectional view of blocks in a tray, showingremoval of a block by finger contact 7 through a hole in the tray,

FIGURES 8 through 13 are central, sectional views through a series ofmodified blocks,

FIGURE 14 is a top plan view of the block of which FIGURE 13 is asection, and

FIGURE 15 is a top plan view, on reduced scale, ofa row of blocksreceived on the assembly rod.

Referring to the drawings by characters of reference, there is shown, inFIGURE 1, a square tray 10 of dished form, dimensioned to snugly receivean array of individual square blocks 12 comprising 10 rows and 10columns, and bearing all of the respective two-digit combinations from00 to 99, the arrangement being such that no digit is repeated in eitherthe group of left hand digits or right hand digits in any row or column.As stated above, this is but one of many possible solutions, and ismerely illustrated herein to demonstrate the background of theinvention.

In working up to a solution, the puzzler will deal with a whole row or awhole column ata time. Heretofore this has involved repeated erasuresand rewrites of tentative combinations or an excessive and bewilderinguse of scratch paper. By my invention I set up such groups byarrangement of discrete, durable units bearing permanent symbols andprovide means to maintain position and orientation of the units in thegroup and to handle and transfer the group, as required.

Thus, in FIGURE 2 there is shown a square block 14 from which thesymbols have been omitted to more clearly show the pair of centrallyarranged, horizontal, mutually perpendicular, through passages, 16 and18, of square cross-section. Shown adjacent the block, in alignment withpassage 18, is an assembly rod or skewer 20 of square cross-sectionsized to be slidably received in either of passages 16 or 18, and havinga ring-form handling head 22. The particular cross-section of thepassages and of the skewer may be widely varied, the essentialrequirement being that they be non-circular, so that when a series ofblocks are assembled on the rod, as in. FIGURE 15, the blocks will notturn on the rod, but will remain with their working surfaces in a commonplane.

FIGURES 3 and 4 show a composite block in which the two families ofsymbols are characterized by the colors of the block components. Thus,for instance, in the particular block shown, the border area 24 is red,and the central insert 26, received in a shallow recess in the block, isblue. While the insert has been shown as square, it may also becircular, since it does not extend sufiiciently into the depth of theblock to require alignment of sections of the transverse bores. Theinsert 28 of FIGURE 5 on the other hand, which extends through theentire depth of the block, should not be circular. In these figures thetransverse bores 30, 32 are shown as elliptical in section, and theassembly rod will have a similar section.

FIGURE 6 shows how the usefuh'ress of the block, such as in FIGURE 3 maybe extended by placing Arabic numerals on its obverse side.

For minor adjustments of individual blocks after rows and columns havebeen laid out, the tray 10 may be provided with bottom openings 34, asshown in FIGURE 7, through which the finger of the puzzler may beinserted to lift the block 36 from its assembly. It should also be notedthat the vertical wall of the tray has notches 37 in its upper edge toaccommodate the assembly rod 20.

In FIGURE 8 there is shown a section of block similar to that of FIGURE4 in which the insert 38 has an integral, lifting knob 40. In FIGURE 9the insert 42 has a depressed area 44 in one surface, and an integralknob 46 in said area and flush with said surface. Another lift means isshown in FIGURE 10 wherein an insert 43 of magnetic material is embeddedin a block 50. If the skewer is made of steel it may be used to liftthis type of block. FIGURE 11 shows a similar magnetic insert embeddedin a shallow, block component 52. FIGURE 12 shows a two-component blockas in FIGURE 4, with the magnetic insert embedded in the block proper,54, on the side opposite, the insert 56. FIGURE 13 shows block 58 of thesame general type as that of FIGURE 12 with a ring 60 of magneticmaterial embedded in the block, in surrounding relation to the cavity 62for the insert. It will be understood, of course, that the metal insertsneed not be magnetic if an outside magnet is used. For this purpose, theskewer may be magnetic.

With the foregoing description it is believed that the manner of use ofthe device will be fairly obvious. As one phase of the working out ofthe solution, the opera tor Will concentrate on building up eithercolumns or rows, as separate entities. In the gradual selection ofpieces to make up one of these entities, the blocks may be threaded ontothe skewer as selected, or they may be loosely laid out on a table untilthe proper arrangement is achieved, and then all blocks in the row orcolumn slipped onto the skewer. In either case, hey are arranged withthe symbols employed (i.e., colors or numbers or letters) all facing inone direction, and due to the keying action between the skew-er and thepassage, this orientation is maintained in the handling of the groupuntil the group has been laid in place inthe master square (or tray) andthe skewer withdrawn, after which any required handling of individualblocks may be effected by appropriate devices, such as the knobs,magnetic inserts and holes in the tra as shown.

While certain preferred embodiments have been shown and described, theseare not limiting, since various modifications, such as alterations,additions and substitution of reasonable equivalents, will be suggestedto those skilled in the art in the light of this disclosure, and theinvention should not, therefore, be deemed as limited, except as shallappear from the spirit and scope of the appended claims.

I claim:

.1. For use in solving puzzles of the magic square type,

a plurality of rectangular blocks, each bearing a pair of symbols on atleast one face, and said pairs being dissimilar throughout the blocks,said blocks each having at least one passage of oblong cross-sectionextending between a pair of opposite edges of the block, at least oneassembly rod of oblong cross-section adapted to mate with said passagesin sliding relationship, and a rectangular tray with vertical, marginalwalls to receive the assembled blocks, said walls having notches toaccommodate the assembly rod.

For use in solving puzzles of the magic square type, a plurality ofrectangular blocks, each bearing a pair of symbols on at least one face,and said pairs being dissimilar throughout the blocks, said blocks eachhaving at least one passage of oblong cross-section extending between apair of opposite edges of the block, at least one assembly rod of oblongcross-section adapted to mate with said passages in slidingrelationship, and a rectangular tray with vertical, mar inal walls toreceive the assembled blocks, said walls having notches to receive theassembly rod, the bottom or" said tray having openings for access tosaid blocks, to remove them from the tray.

References Cited by the Examiner UNITED STATES PATENTS 196,532 10/77Martin. 470,717 3/92 Sterne 273-153 807,113 12/05 Dyer. 1,100,549 6/14Elkins 273-137 1,233,544 7/17 Bissey 35-73 1,959,040 5/34 Schilling273-153 2,377,100 5/45 Patterson. 2,474,365 6/49 Munn 273-137 X2,493,435 1/50 Archarnbault 46-26 2,795,427 6/57 Sachs 273-153 2,824,7402/58 Cowan 273-137 2,932,518 4/60 Burros 273-137 FOREIGN PATENTS 132,2847/51 Sweden.

DELBERT B. LOWE, Primary Examiner.

ELLIS E. FULLER, LEONARD W. VARNER,

Examiners.

1. FOR USE IN SOLVING PUZZLES OF THE MAGNETIC SQUARE TYPE, A PLURALITYOF RECTANGULAR BLOCKS, EACH BEARING A PAIR OF SYMBOLS ON AT LEAST ONEFACE AND SAID PAIRS BEING DISSIMILAR THROUGHOUT THE BLOCKS, SAID BLOCKSEACH HAVING AT LEAST ONE PASSAGE OF OBLONG CROSS-SECTION EXTENDINGBETWEEN A PAIR OF OPPOSITE EDGES OF THE BLOCK, AT LEAST ONE ASSEMBLY RODOF OBLONG CROSS-SECTION ADAPTED TO MATE WITH SAID PASSAGES IN SLIDINGRELATIONSHIP, AND A RECTANGULAR TRAY WITH VERTICAL, MARGINAL WALLS TORECEIVE THE ASSEMBLED BLOCKS, SAID WALLS HAVING NOTCHES TO ACCOMMODATETHE ASSEMBLY ROD.